Quantum algorithms for colored Jones polynomials

Louis H. Kauffman; Samuel J. Lomonaco Jr.

doi:10.1117/12.821974

27 April 2009 Quantum algorithms for colored Jones polynomials

Louis H. Kauffman, Samuel J. Lomonaco Jr.

Proceedings Volume 7342, Quantum Information and Computation VII; 73420L (2009) https://doi.org/10.1117/12.821974
Event: SPIE Defense, Security, and Sensing, 2009, Orlando, Florida, United States

Abstract

We review the q-deformed spin networks and apply these methods to produce unitary representations of the braid groups that are dense in the unitary groups. The simplest case of these models is the Fibonacci model, itself universal for quantum computation. We formulate these braid group representations in a form suitable for computation and algebraic work and apply them to quantum algorithms for the computation of colored Jones polynomials and the Witten-Reshetikhin-Turaev Invariants.

Citation Download Citation

Louis H. Kauffman and Samuel J. Lomonaco Jr. "Quantum algorithms for colored Jones polynomials", Proc. SPIE 7342, Quantum Information and Computation VII, 73420L (27 April 2009); https://doi.org/10.1117/12.821974

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